castigate
To scold someone very harshly, often in public.
To castigate means to criticize someone severely and harshly, often in public. When a coach castigates a player for missing practice, he's delivering a stern, forceful scolding that makes clear how seriously wrong the behavior was, going far beyond simply pointing out a mistake.
The word carries weight beyond ordinary criticism. If your teacher says “please try harder on your homework,” that's feedback. But if she castigates you for copying someone else's work, she's expressing strong disapproval with sharp, stinging words meant to make you feel the gravity of what you did.
Castigate often involves public criticism. A newspaper might castigate a politician for breaking promises, or a principal might castigate students at an assembly for vandalism. The public nature can make it more humbling and memorable.